Yet Grand Slams are best-of-five set matches which require more endurance than the best-of-three staple found week in and out on tour.
"If we expect this guy to win majors now, I think that's a bridge too far unless he addresses the physical gap between him and the other guys," four-times Grand Slam champion Courier said on the Tennis Channel at the BNP Paribas Open in Indian Wells, California.
"But from a talent, shotmaking showpoint, he showed there is no gap there, because that was a tough draw he went through."
Kyrgios has a 6-6 combined record against Novak Djokovic, Roger Federer and Nadal, a statistic that does not surprise Courier.
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"Those are pressure-free matches for him. He has that first strike ability to take the racket out of their hands with his serve and then he can shock-absorb with his backhand.
"He's dangerous but he's also dangerous to himself at times in the matches on outside court when he goes walkabout like an Aussie can, and he's not as focused."
The 23-year-old Kyrgios jumped to 33rd in the world with his Acapulco win.
He is seeded 31st at Indian Wells, giving him the luxury of a first-round bye, though he could meet top seed Djokovic in the third round.
First-round men's matches begin on Thursday.
"Big picture, it's nice to see him engaged," said Courier, who recently stepped down after eight years as United States Davis Cup captain.
"Hope this (Acapulco title) is a kick starter for him."
(Reporting by Andrew Both in Cary, North Carolina; Editing by Toby Davis)
